名校
解题方法
1 . 已知集合M是具有以下性质的函数
的全体:对于任意s,
都有
,且
.给出下列四个结论:
①函数
属于M;
②函数
属于M;
③若
,则
在区间
上单调递增;
④若
,则对任意给定的正数s,一定存在某个正数t,使得当
时,恒有
.其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8befb3495a66413e55880ae8a151c308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0035bf4d1cd0978e745d32536e78cb.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1be9a7177c28cc52018fddf300e5b37.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa79911431b66a96b4fa51a4e4fb6098.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3ea0467dc6393d7c4b602175a394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3ea0467dc6393d7c4b602175a394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caf2c1a28e672e271d70d6e0048e4f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973007637e515cb5c0737e646f8f4cc8.png)
您最近一年使用:0次
2023-08-02更新
|
544次组卷
|
4卷引用:北京市清华附中2022-2023学年高二下学期期末数学试题
北京市清华附中2022-2023学年高二下学期期末数学试题【北京专用】专题14(一轮复习)集合与常用逻辑(第一部分)-高二上学期名校期末好题汇编(已下线)专题4.9 指数函数与对数函数全章综合测试卷(提高篇)-举一反三系列(已下线)第四章 指数函数与对数函数-【优化数学】单元测试能力卷(人教A版2019)
名校
2 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
566次组卷
|
5卷引用:北京市顺义区2022-2023学年高一下学期期末质量监测数学试题
北京市顺义区2022-2023学年高一下学期期末质量监测数学试题重庆市南开中学校2023-2024学年高一上学期开学考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
3 . 设
,对定义在
上的函数
,若存在常数
,使得
对任意
恒成立,则称函数
满足性质
.
(1)判断下列函数是否具有性质
?
①
,②
,③
.
(2)若函数
具有性质
,其中
,求证:函数
具有性质
;
(3)设函数
具有性质
,其中
是奇函数,
是偶函数.若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3281ac9e36c20d31cf4bc12548b46f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)判断下列函数是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40dbde013dc2c216be25e00d265fd66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736e6a8b3201d57d57d5ccd9613664d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd158c168d914102b14f608d9ed61a33.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc14f4aa8998324c2b74594beaabb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1686e7fc606fe72d46948677016bf7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8037e4a9f4aadfef393b556f12a83e5.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa485d54469db584da4fc33346fd92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb95973233ce656c0a22569078955644.png)
您最近一年使用:0次
4 . 对于定义在
上的函数
和正实数
若对任意
,有
,则
为
阶梯函数.
(1)分别判断下列函数是否为
阶梯函数(直接写出结论):
①
;②
.
(2)若
为
阶梯函数,求
的所有可能取值;
(3)已知
为
阶梯函数,满足:
在
上单调递减,且对任意
,有
.若函数
有无穷多个零点,记其中正的零点从小到大依次为
直接给出一个符合题意的a的值,并证明:存在
,使得
在
上有4046个零点,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dac54fb389586d807774374eaec169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2a101cad2f3b40df6e270c877f7f6e.png)
(1)分别判断下列函数是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d71f56ef6906bc37ca312051d97d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2a101cad2f3b40df6e270c877f7f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2a101cad2f3b40df6e270c877f7f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e37b06259c516fa61e609615635b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9aef6fb4e84ba3a07d196117b931e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a124a601cdca9686ac0d10b0e381c090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d767cba8f37ccd4b40efec40dd430e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24f8613f617dec212dd31a5cbde610c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb14c1f4dc23cb15710c30271104d0d6.png)
您最近一年使用:0次
2023-07-10更新
|
694次组卷
|
2卷引用:北京市西城区2022-2023学年高一下学期期末考试数学试题
名校
5 . 设
,已知由自然数组成的集合
,集合
,
,…,
是
的互不相同的非空子集,定义
数表:
,其中
,设
,令
是
,
,…,
中的最大值.
(1)若
,
,且
,求
,
,
及
;
(2)若
,集合
,
,…,
中的元素个数均相同,若
,求
的最小值;
(3)若
,
,集合
,
,…,
中的元素个数均为3,且
,求证:
的最小值为3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1221e342a03bd2806e0993c996827ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abc7b7ef8b7a91099ca63ea1aaf7cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6571a9572dc91c90da43a5390f69d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b2c4a940739711008be65a1fad4146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ac1a105450fef08656cf15a10e7fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47771d50cf28b8f528afda24720eb8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52ce6355f8b297a89f20f2e7f48041d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beea8e2b24bdc221f6c16e46efdf665.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862353b1d19b5e38a60c4ceeb2b01913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4e4ea995fa993d6a55c2e523fa8ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad28732b9ef03fa2a2fcabe344c27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caddd958ae597c7a1f8f6a9ee2a3200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194592cb77de8a597d5d64e1c85c3249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece66a27e197695e0f02e1a0afa4a0d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
您最近一年使用:0次
2023-07-10更新
|
683次组卷
|
4卷引用:北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题
北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题北京市陈经纶中学2023-2024学年高二上学期开学检测数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
6 . 已知三角形
是边长为
的等边三角形.如图,将三角形
的顶点
与原点重合.
在
轴上,然后将三角形沿着
轴顺时针滚动,每当顶点
再次回落到
轴上时,将相邻两个
之间的距离称为“一个周期”,给出以下四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/ea6ae40c-45cb-442b-8319-937a33b2477f.png?resizew=172)
①一个周期是
;
②完成一个周期,顶点
的轨迹是一个半圆;
③完成一个周期,顶点
的轨迹长度是
;
④完成一个周期,顶点
的轨迹与
轴围成的面积是
.
其中说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/ea6ae40c-45cb-442b-8319-937a33b2477f.png?resizew=172)
①一个周期是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
②完成一个周期,顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
③完成一个周期,顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b03f3d13783ee2cb12a81ce6fd07b.png)
④完成一个周期,顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b03f3d13783ee2cb12a81ce6fd07b.png)
其中说法正确的是( )
A.①② | B.①③④ | C.②③④ | D.①③ |
您最近一年使用:0次
解题方法
7 . 设全集
,集合A是U的真子集.设正整数
,若集合A满足如下三个性质,则称A为U的
子集:
①
;
②
,若
,则
;
③
,若
,则
.
(1)当
时,判断
是否为U的
子集,说明理由;
(2)当
时,若A为U的
子集,求证:
;
(3)当
时,若A为U的
子集,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fefd9d7303a04708b4f2d728e78361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed0c7122ffdbf145d72a310671465fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0412e8d25fa4748e3f6784611bd61990.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8a1b0b32229f6a9f5b85c11f05bee2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658f2824532e5b72962fe34a22c27c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251a5b0faec4a29eff8173a633c0b765.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8489b7692d3889aede2335c3ac8aca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb76e516509e33dc0d29663cc6b884bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd131b82e404452880d7a97792f22493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7844925f9077aa32c990fc20a51467.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcd23a8020d731bd512bb8df45ea594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e13bbde03ffad05ecc3fee8120b6a6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575c2057865186fb80a50f67ee6ea70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
您最近一年使用:0次
2023-01-06更新
|
899次组卷
|
10卷引用:北京市朝阳区2022-2023学年高一上学期数学期末试题
北京市朝阳区2022-2023学年高一上学期数学期末试题北京市第五十七中学2022-2023学年高一(1+3科技创新试验班)下学期期中考试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)专题03集合的运算-【倍速学习法】(人教A版2019必修第一册)(已下线)第一章 集合与常用逻辑用语(单元提升卷)-【满分全攻略】(人教A版2019必修第一册)(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列(已下线)FHsx1225yl138
名校
8 . 设有限集合
,对于集合
,给出两个性质:
①对于集合A中任意一个元素
,当
时,在集合A中存在元素
,使得
,则称A为
的封闭子集;
②对于集合A中任意两个元素
,都有
,则称A为
的开放子集.
(1)若
,集合
,判断集合
为
的封闭子集还是开放子集;(直接写出结论)
(2)若
,且集合A为
的封闭子集,求
的最小值;
(3)若
,且
为奇数,集合A为
的开放子集,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d3d592c03146bab0e93fee04ad3072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e827f67d8b6f601f25c39c0116abda42.png)
①对于集合A中任意一个元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6f4f0f0f629dae342af9261c006de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17748c68c2a8a738c52175ebaa2f5e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247d742bdd34642e1da9fe9161e3a637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
②对于集合A中任意两个元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a843998f766e61f7abbdd2e985bad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb52fdd006724b2dfdb7e6988f813ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb2ad93be53f0838c8563903ad31b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20a5ff55592f7eea41b0ef0d8cd7f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a994566930068fd6edf5342c69bc25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e586121ce8e638b9d8da6d3a00f308ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-01-06更新
|
754次组卷
|
9卷引用:北京市昌平区2022-2023学年高一上学期期末质量检测数学试题
北京市昌平区2022-2023学年高一上学期期末质量检测数学试题北京市第一六六中学2022-2023学年高一下学期阶段性诊断考试数学试题北京市第一六六中学2022-2023学年高一下学期3月月考数学试题(已下线)1.1集合的概念(分层作业)-【上好课】(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(人教A版2019必修第一册)(已下线)专题02集合间的基本关系2-【倍速学习法】(人教A版2019必修第一册)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
解题方法
9 . 设函数
的定义域为D,对于区间
,若满足以下两条性质之一,则称I为
的一个“
区间”.
性质1:对任意
,有
;
性质2:对任意
,有
.
(1)分别判断区间
是否为下列两函数的“
区间”(直接写出结论);
①
; ②
;
(2)若
是函数
的“
区间”,求m的取值范围;
(3)已知定义在
上,且图象连续不断的函数
满足:对任意
,且
,有
.求证:
存在“
区间”,且存在
,使得
不属于
的所有“
区间”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a67b23b778224005c7bf0097ff488f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
性质1:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1e560364dea022693928309250f158.png)
性质2:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51dc07201b5f984fafd2cf968bec88ff.png)
(1)分别判断区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb68ccf2d913a83e68df3524263aa8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85410ff00c81839ff9a64bf86dc36f5e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301bacc282b75b95f9bee92a618d544f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4cd02b69b76000f9b9826d9929a324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd809d14a09c538823c43745fe3aee13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ad90ca228230b03f12eb48ee0c1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
您最近一年使用:0次
2023-01-05更新
|
865次组卷
|
5卷引用:北京市西城区2022-2023学年高一上学期数学期末试题
北京市西城区2022-2023学年高一上学期数学期末试题湖南省衡阳市衡钢中学2022-2023学年高一下学期开学考试数学试题上海市行知中学2023-2024学年高一上学期第二次质量检测(12月)数学试题(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本(已下线)上海市浦东新区华东师范大学第二附属中学2023-2024学年高一上学期期末质量检测数学试卷
名校
解题方法
10 . 对于非空数集A,若其最大元素为M,最小元素为m,则称集合A的幅值为
,若集合A中只有一个元素,则
.
(1)若
,求
;
(2)若
,
,求
的最大值,并写出取最大值时的一组
;
(3)若集合
的非空真子集
两两元素个数均不相同,且
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d2ec1a5112ce091f604a70db6ff070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91daec4d6f087fd9575aaf6556489f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bfdfd1a175a860a18587e4c21e04da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d70d5962157e2116e7f1a267153967.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb78779234085b9dbec4e3424a1a4971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819a9ba7e6e80c06082fd1af18f7f43e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e45173688d37986ac521cbe53d22ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a227a694dc404d1184578c7d278fd8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4f1149c86913354c231ad31e01fccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f61b74f81868a14729e49b982246e.png)
您最近一年使用:0次
2023-01-04更新
|
827次组卷
|
7卷引用:北京市东城区2022-2023学年高一上学期期末统一检测数学试题
北京市东城区2022-2023学年高一上学期期末统一检测数学试题北京市第一零九中学2023-2024学年高一上学期12月月考数学试卷北京市第二十五中学2023-2024学年高一上学期期中过程性评价数学试题河北省邯郸市魏县2022-2023学年高一上学期期末考试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列重庆市沙坪坝区部分学校2023-2024学年高一上学期9月检测(一)数学试题(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列